Matroids, Matrices, and Partial Hyperstructures
Loading...
Author(s)
Zhang, Tianyi
Advisor(s)
Lorscheid, Oliver
Editor(s)
Collections
Supplementary to:
Permanent Link
Abstract
This thesis studies the application of algebra and algebraic geometry to matroid theory. Baker
and Bowler developed the notions of weak and strong matroids over tracts. Later, Baker and
Lorscheid developed the notion of foundation of a matroid, which characterize the representability
of the matroid. We study a variety of topics under this theme. In chapter 2, we provide a condition
which is sufficient to guarantee that the notions of strong and weak matroids coincide. In chapter 3,
we describe a software program that computes all representations of matroids over a field, based on
the theory of foundations. In chapter 4, we define a notion of rank for matrices over tracts in order
to get uniform proofs of various results about ranks of matrices over fields.
Sponsor
Date
2023-07-17
Extent
Resource Type
Text
Resource Subtype
Dissertation